Nobuyuki Takahashi (Hokkaido University) Ryoichi Onoda (Hokkaido University)

The effect of common knowledge – Why do people cooperate more when they face

a social dilemma situation where mutual cooperation yields restoration of fairness?

Nobuyuki Takahashi (Hokkaido University)Ryoichi Onoda (Hokkaido University)Hikaru Hamada (Hokkaido University)Rie Mashima (Kumamoto Gakuen University)

E-mail: [email protected]

ICSD2009Kyoto

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Introduction

There have been many collective behaviors in human history.

Collective behaviors seem to be thrived when the purpose is the restoration of fairness (e.g., civil rights movements, anti-Vietnam War movements).

Why?

Many collective behaviors involve social dilemmas. So, isn’t free-riding still the better option than participating in a social movement?

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Takezawa (1999)

Ordinary one-shot PGG

3) Expectation of others’ cooperation in one-shot public goods game (PGG)

Provision of PG restores fairness<

Since expectation of others’ cooperation promotes cooperation,4) Cooperation rate

Ordinary one-shot PGG Provision of PG restores fairness<

1) Experience of unfairness invokes the sense that unfairness is shared among the other people.

2) The goal changes from pursuing self-interest to jointly restoring fairness.

Why does the experience of unfairness promote expectation of others’ cooperation?

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Takezawa (1999)

The sense of fairness activates the common knowledge that everybody was treated unfairly.

This common knowledge induces higher level of expectation that leads to higher level of cooperation.

Why does this process occur?Why is the expectation of others’ cooperation higher when participants were all treated unfairly?

Taken for granted, but…

According to Takezawa (1999)…

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What affects expectation?

Two reasons to defect in SD (e.g., Dawes et al. 1986; Van Lange et al. 1992; Yamagishi & Sato 1986)

(1) Greed – the temptation to free-ride

Not greed but fear affects expectation of others’ cooperation.

(2) Fear – the prospect that one's cooperation may be exploited

However, there can be at least two sources of fear.

Fear of greedFear of fear

What is the function of being treated unfairly?

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Revisiting Takezawa (1999)

Two possibilitiesWhat is the function of being treated unfairly?

(1) Reduction of fear of greed – People expect that the experience of unfairness transforms the goal of other people from maximizing self-interest to achieving mutual cooperation in order to restore fairness.

The other people will cooperate because they are no longer greedy.

We want to restore fairness!

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Two possibilitiesWhat is the function of being treated unfairly?

We want to restore fairness!However, this may not be sufficient to induce cooperation.

But the other people may still defectbecause of fear.

Fear of fear

(1) Reduction of fear of greed – People expect that the experience of unfairness transforms the goal of other people from maximizing self-interest to achieving mutual cooperation in order to restore fairness.

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(2) Reduction of fear of fear – Perception of unfairness makes people expect that the other people’s fear of greed was reduced.

Reducing fear of fear requires that the fact that everyone was treated unfairly is a common knowledgecommon knowledge.

The other people will cooperate because they have no fear.

The others are no longer greedy!

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Main purpose of the study

To differentiate these two functions and see if reduction of fear of fear is necessary for inducing higher level of cooperation

Manipulation: Whether or not the fact that everybody was treated unfairly is a common knowledge

Reduction of fear of greed: Privately knowing that everybody was treated unfairly is enough

Reduction of fear of fear: The fact that everybody was treated unfairly must be a common knowledge

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Experiment

3) Private knowledge condition : The same as Common knowledge condition. The only difference is that only the participants knew that everybody was treated unfairly by a dictator, and that they could restore fairness by achieving mutual cooperation in PGG.

One factor, between-subjects design

1) Control condition : Ordinary one-shot PGG without any context

2) Common knowledge condition : One-shot PGG that is identical with Control condition. However, before playing the game, participants were all treated unfairly by a dictator and they could restore fairness by achieving mutual cooperation in PGG.

Participants : 125 undergraduate students (M: 68, F: 56, UK: 1)

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1) Control condition

1st stage: Social inference task (a bogus task)

Each player was paid 500 yen ($5) for completing the task.

Ordinary one-shot PGG without any context

Social inference task

500 yen

500 yen

500 yen

500 yen

500 yen

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1) Control condition

2nd stage: One-shot step-level PGG

Ordinary one-shot PGG without any context

Cooperation : Provide 500 yen to the groupDefection : Keep 500 yen for oneself

500 yen

500 yen

500 yen

500 yen

500 yen

If more than 3 players cooperate,

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1) Control conditionOrdinary one-shot PGG without any context

500 yen

If more than 3 players cooperate, a public good (4000 yen) is provided.

4000 yen



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500 yen

Total earnings of cooperators : 500-500+(4000/5)=800 yen defectors : 500-0+(4000/5)=1300 yen

4000 yen

C C C CD

800 yen

800 yen

800 yen

800 yen

800 yen



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500 yen

500 yen

500 yen

500 yen

500 yen

If less than 4 players cooperate,



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500 yen

500 yen

500 yen

If less than 4 players cooperate, a public good is not provided.

0 yen



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500 yen

500 yen

500 yen

If less than 4 players cooperate, a public good is not provided.

0 yen



Deception

Although participants were told that there were other participants and that they would interact with them, actually each participant behaved as an individual. In other words, there was no real interaction among the participants.

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2) Common knowledge condition

1st stage: Social inference task (a bogus task)

As a 6-person group, players were paid 7000 yen ($70) for completing the task.

Identical incentive structure with the one in the other 2 conditions

Social inference task

7000 yen

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After 1st stage (before 2nd stage): Dictator gameA dictator was chosen randomly from the group and

decided to allocate 7000 yen among group members.


7000 yen

? yen

? yen

? yen

? yen

? yen

Dictator

Recipient Recipient Recipient Recipient Recipient

Participant

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7000 yen

? yen

? yen

? yen

? yen

? yen

Dictator


Participant

Since we used deception, however, actually a dictator and the other recipients did not exist. Only a participant was a real person. Also, dictator’s decision was predetermined by the experimenter.

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4500 yen

500 yen

500 yen

500 yen

500 yen

500 yen

Dictator


Participant

The dictator allocated 4500 yen for himself and 500 yen for each of the other 5 players.

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2nd stage: One-shot step-level PGG to restore fairness

5 recipients were asked if they want to provide 500 yen.


4500 yen

500 yen

500 yen

500 yen

500 yen

500 yen

Dictator


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2) Common knowledge conditionIdentical incentive structure with the one in the other 2 conditions

4500 yen

500 yen

500 yen

500 yen

500 yen

500 yen

Dictator

C C C C D

If more than 3 recipients cooperate,


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500 yen

500 yen

DictatorIf more than 3 recipients cooperate, 4000 yen was forfeited from the dictator,

4000 yen

C C C C D


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500 yen

4000 yen

500 yen

DictatorIf more than 3 recipients cooperate, 4000 yen was forfeited from the dictator, and recipients share 4000 yen equally.


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500 yen

500 yen

DictatorIf more than 3 recipients cooperate, 4000 yen was forfeited from the dictator, and recipients share 4000 yen equally.

800 yen

800 yen

800 yen

800 yen

800 yen

Total earnings of cooperators : 500-500+(4000/5)=800 yen defectors : 500-0+(4000/5)=1300 yen

C C C C D


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4500 yen

500 yen

500 yen

500 yen

DictatorIf less than 4 recipients cooperate, nothing happens.

D D C C D

Total earnings of cooperators : 500-500=0 yen defectors : 500-0=500 yen


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3) Private knowledge conditionIdentical with Common knowledge condition

The only difference is that participants are the only one who knew that everybody was treated unfairly.

After the dictator allocated 7000 yen, each player received an allocation sheet that only says how much she was allocated by the dictator.

? yen

500 yen

? yen

? yen

? yen

? yen

Dictator


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3) Private knowledge condition

? yen

500 yen

? yen

? yen

? yen

? yen

Dictator


By lottery one player was chosen as a person who could see the complete distribution of 7000 yen.

Identical with Common knowledge condition



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4500 yen

500 yen

500 yen

500 yen

500 yen

500 yen

Dictator



The recipient who was chosen by lottery knew that the other recipients did not have full information.

She knew that she was the only person who knew how much each person received from the dictator.

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4500 yen

500 yen

500 yen

500 yen

500 yen

500 yen

Dictator



The recipient who was chosen by lottery knew that the other recipients did not have full information.

She knew that she was the only person who knew how much each person received from the dictator.

Since we used deception, actually all participants were chosen by lottery.

Participant

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Hypotheses

H1: Only reduction of fear of greed occursParticipants would cooperate more in both Private and Common knowledge conditions than in Control condition.

There are 3 competing hypotheses regarding cooperation rate.

0

10

20

30

40

50

60

Control condition Private knowledgecondition

Common knowledgecondition

Hypothetical result

Cooperation rate

Control Private Common

Privately knowing that everybody was treated unfairly is enough , and common knowledge is unnecessary

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Hypotheses

H2: Only reduction of fear of fear occursParticipants would cooperate more in Common knowledge condition than in Control and Private knowledge conditions.


0

10

20

30

40

50

60



Hypothetical result


Cooperation rate

Privately knowing that everybody was treated unfairly is not enough, and common knowledge is necessary

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Hypotheses

H3: Both reduction of fear of greed and reduction of fear of fear occur.Cooperation rate would be lowest in Control condition and highest in Common knowledge condition.


0

10

20

30

40

50

60



Hypothetical result


Cooperation rate

Both privately knowing that everybody was treated unfairly and common knowledge promote cooperation.

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Result (1) Cooperation rate

30.56 28.21

54

0

10

20

30

40

50

60

Control Private knowledge Common knowledge%

Figure 1: Cooperation rate in each condition

Dummy for Private knowledge condition: β = -0.11, n.s.Dummy for Common knowledge condition: β = 0.98, p<.05

Participants cooperated more in Common knowledge condition than in the other two conditions.

Hypothesis 2 was supported.

Control Private CommonLogistic regressionDV: Cooperation=1, Defection =0 IV: Dummy for Private knowledge cond, Dummy for Common knowledge cond *Reference category – Control condition

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Result (2) Effect of expectation

The effect of common knowledge disappeared when we controlled expectation.

Independent variable Model 1 Model 2 Model 3

Dummy for Private knowledge -0.11 -0.71 -1.25+Dummy for Common knowledge

0.98* 0.34 0.01

Expected cooperation rate - 26.82 ** -Estimated probability of the provision of a public good

- - 0.07*

Participants cooperated more in Common knowledge condition because they expected more cooperation by the others.

This result suggests that reduction of fear promoted cooperation

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Participants cooperated more in Common knowledge condition than in the other conditions.

Summary and Conclusion

Participants cooperated more only when they knew that the other participants knew that everybody was treated unfairly.

Summary

Unfair treatment must be a common knowledge in order to induce a higher level of cooperation. This is because such a common knowledge reduces fear of fear rather than fear of greed.

Conclusion

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Future directions

Are there any factors other than the sense of unfairness that promote cooperation by reducing fear of fear through automatically activating the perception of common knowledge?

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Thank you for your attention.

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Hypotheses

(1) Participants would cooperate more in the unfair treatment conditions (private and common knowledge conditions) than in the control condition.

Cooperation rate

The effect of unfair treatment by the dictator

(2) Participants would cooperate more in the common knowledge condition than in the private knowledge condition.

The effect of common knowledge

Private knowledge condition

Common knowledge condition > Control condition

Private knowledge conditionCommon knowledge condition>

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Result (1) Cooperation rate

30.56 28.21

54

0

10

20

30

40

50

60



%

Figure 1: Cooperation rate in each condition

Dummy for Private knowledge condition: β = -1.09, p<.05Dummy for Control condition: β = 0.98, p<.05

Participants cooperated more in Common knowledge condition than in the other two conditions.

Hypothesis 2 was supported.

Logistic regression

Dependent variable: Cooperation=0, Defection =1

Independent variable: Dummy for Private knowledge condition Dummy for Control condition

Common knowledge condition – Reference category

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Experiment

5 players per group

Players first engaged in a social inference task (bogus task), and were paid 500 yen ($5) for completing the task.

Players were then asked if they want to provide 500 yen to the group.

If more than 3 players provided 500 yen to the group, everybody received 800 yen as a bonus. Cooperators receive 800 yen and defectors receive 1300 yen.

If less then 4 players provided 500 yen, then nobody received a bonus. Cooperators receive 0 yen and defectors receive 500 yen.

Control condition : Ordinary one-shot SD without any context

We used deception: Although participants were told that there were other participants and that they would interact with them, actually each participant behaves as an individual. In other words, there was no real interaction with the other participants.

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Experiment

2nd stage: One-shot step level SD

Control condition : Ordinary one-shot SD without any context


500 yen

500 yen

500 yen

500 yen

500 yen

If more than 3 players cooperate, a public good (4000 yen) is provided.Total earnings of cooperators : 500-500+(4000/5)=800 yen defectors : 500-0+(4000/5)=1300 yen

If less then 4 players cooperate, a public good is not provided.Total earnings of cooperators : 500-500=0 yen defectors : 500-0=500 yen

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Experiment

6 players per group

Players first engaged in a social inference task (bogus task), and were paid 7000 yen as a group.

A dictator was chosen randomly from the group and decided to allocate 7000 yen among group members.

The dictator allocated 4500 yen for himself and 500 yen for each of the other 5 players.

5 players were then asked if they want to provide 500 yen.

If more than 3 players provided 500 yen to the group, 4000 yen was forfeited from the dictator and the other 5 players shared 4000 yen equally. In other words, each player received 800 yen.

If less then 4 players provided 500 yen, then nothing happens.

Common knowledge condition

Incentive structure is identical with the one in the other conditions.

Successful restoration of fairness

Unsuccessful restoration of fairness

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Experiment


The only difference is that participants are the only one who knew that everybody was treated unfairly by the dictator.

Private knowledge condition

Since we used deception, actually all participants were chosen by lottery.

After the dictator allocated 7000 yen, each player received an allocation sheet that says how much she was allocated by the dictator.

However, how much the other players’ received was not written on the allocation sheet.

Then, by lottery one player was chosen as a person who could see the complete distribution of 7000 yen.

Incentive structure is identical with the one in the other conditions.

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Result (2) Effect of 2nd-order expectation

What is your estimate of the other participants’ estimate of the probability that more than 3 participants provided the money?

0

0.1

0.2

0.3

0.4

0.5

0.6

Controlcondition

Privateknowledgecondition

Commonknowledgecondition

F（ 2,124） =6.66, p<.01

2nd-order expectation (expectation on expectation) was lower in Control condition than in the other 2 conditions.

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Result (2) Effect of 2nd-order expectation

The effect of common knowledge disappeared when we controlled 2nd-order expectation.

Participants cooperated more in Common knowledge condition because they expected the other participants’ expectation of cooperation higher.

Independent variable Model 1 Model 2

Private knowledge -0.11 -1.00

Common knowledge 0.98* 0.24

2nd-order expectation - 0.04 **

Reduction of fear of fear plays a critical role.

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Result (2) Effect of expectation

1.86

2.23

2.71

0

1

2

3

4



What is your estimation of the probability that more than 3 participants provided the money?

How many participants do you think have provided the money?

0

0.1

0.2

0.3

0.4

0.5

0.6

Controlcondition

Privateknowledgecondition

Commonknowledgecondition

F（ 2,124） =5.11, p<.01 F（ 2,123） =3.43, p<.05

Participants’ expectation was higher in Common knowledge condition than in Control condition.

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Participants cooperated more in Common knowledge condition than in the other conditions.

Discussion

Participants cooperated more only when they knew that the other participants knew that everybody was treated unfairly.

2nd-order expectation plays a critical role

Being treated unfairly makes people believe that it is a common knowledge.

Nobuyuki Takahashi (Hokkaido University) Ryoichi Onoda (Hokkaido University)

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